Proofs of the Parisi and Coppersmith-Sorkin random assignment conjectures
Random Structures & Algorithms
Size and Weight of Shortest Path Trees with Exponential Link Weights
Combinatorics, Probability and Computing
The weight and hopcount of the shortest path in the complete graph with exponential weights
Combinatorics, Probability and Computing
Average-Case Analyses of Vickrey Costs
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
The longest minimum-weight path in a complete graph
Combinatorics, Probability and Computing
Viral processes by random walks on random regular graphs
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Approximating the statistics of various properties in randomly weighted graphs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
First passage percolation on the erdős-rényi random graph
Combinatorics, Probability and Computing
Asynchronous rumor spreading in preferential attachment graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
All-pairs shortest paths in O(n2) time with high probability
Journal of the ACM (JACM)
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Consider the minimal weights of paths between two points in a complete graph Kn with random weights on the edges, the weights being, for instance, uniformly distributed. It is shown that, asymptotically, this is log n/n for two given points, that the maximum if one point is fixed and the other varies is 2 log n/n, and that the maximum over all pairs of points is 3 log n/n.Some further related results are given as well, including results on asymptotic distributions and moments, and on the number of edges in the minimal weight paths.